2D phase-unwrapping algorithms (PUAs) are commonly used to obtain a continuous phase map from the sawtooth-shaped phase map. However, implementing PUAs can be time consuming, and the accuracy of those algorithms may be low if there is heavy noise. In this paper, we develop a simple and robust PUA based on the transport of intensity equation (TIE). In our method, the TIE was solved using the fast cosine transform, and a phase correction operation was introduced after the TIE was solved. Because of the phase correction operation, the proposed method can obtain a satisfactory unwrapping result even in a notably hash noise condition. The simulation and experimental results are presented to validate the effectiveness of the proposed method. The detailed software package can be found at https://ww2.mathworks.cn/matlabcentral/fileexchange/68493-robust-2d-phase-unwrapping-algorithm.
This paper proposes a new interferometric method to measure the phase modulation characteristics of a liquid crystal spatial light modulator (LC-SLM). In our proposed method, the beam was incident perpendicular to the SLM and the combined grayscale pattern loaded into the SLM consisted of three parts. The left part was a blazed diffraction grating, and the two right parts were grayscale with different constant values. The gray value in the downward section remained constant at zero, while it gradually increased from 0 to 255 in the upward section. By changing the gray value of the combined grayscale loaded on the LC-SLM, different sheared fringe patterns, generated by the interference between the constant phase-modulated beam and the +1 order diffracted beam of the blazed grating, could be obtained. The phase modulation value could then be calculated using only one sheared fringe pattern. As a result, our proposed method can reduce the effect of environmental vibration or air turbulence and improve measurement precision. The experimental results are presented to validate the method's potential.
Phase unwrapping is a crucial process to obtain the absolute phase profile in many optical phase measurement techniques such as interferometry, holography, profilometry, etc. In this paper, we have studied several phase unwrapping algorithms based on solving the discrete Poisson equation. The differences among those algorithms lie in two aspects: one is the calculation of the input for the Poisson equation using the wrapped phase data and the other is the way to compute the output (unwrapped phase data) using the corresponding input. Firstly, the method to compute the input for the Poisson equation was investigated using the finite difference and fast Fourier transform (FFT) methods. Then different methods, based on FFT or discrete cosine transform, were employed to calculate the unwrapped phase, and their performances were compared in terms of accuracy and efficiency. To enhance the precision of those algorithms, an iteration strategy was introduced and its performance was investigated under different noise conditions. Finally, several pieces of real phase data was tested by using the direct and iterative methods. The detailed software package can be found online (www.mathworks.com/matlabcentral/ fileexchange/71810-phase-unwrapping-algorithms-by-solving-the-poisson-equation).
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